[tsimionescu]

That's patently false for many classes of problems. We know exactly how to solve the traveling salesman problem, and have for decades, but we're nowhere close to solving a random 1000 city case (note: there are approximate methods that can find good, but not optimal, results on millions of cities). Edit: I should say 1,000,000 city problem, as there are some solutions for 30-60k cities from the 2000s.

And there are good reasons to believe that theorem finding and proof generation are at least NP-hard problems.

[vlovich123]

We're not talking about mathematical optimality here, both from the solution found and for the time taken. The point is whether this finds results more cheaply than a human can and right now it's better on some problems while others it's worse. Clearly if a human can do it, there is a way to solve it in a cheaper amount of time and it would be flawed reasoning to think that improving the amount of time would be asymptotically optimal already.

While I agree that not all problems show this kind of acceleration in performance, that's typically only true if you've already spent so much time trying to solve it that you've asymptoted to the optimal solution. Right now we're nowhere near the asymptote for AI improvements. Additionally, there's so many research dollars flowing into AI precisely because the potential upside here is nowhere near realized and there's lots of research lines still left to be explored. George Hinton ended the AI winter.

[visarga]

> The point is whether this finds results more cheaply than a human can

If you need to solve 1000 problems in 3 days you wouldn't find the humans that can do it. So it would not be cheaper if it's not possible.

[vlovich123]

Well if it takes 10% of all of Google’s servers 3 days to solve, you may find it difficult to scale out to solving 1000 problems in 3 days as well.

As for humans, 100 countries send 6 students to solve these problems. It also doesn’t mean that these problems aren’t solvable by anyone else. These are just the “best 6” where best = can solve and solve most quickly. Given a three day budget, 1000 problems could reasonably be solvable and you know exactly who to tap to try to solve them. Also, while the IMO is difficult and winners tend to win other awards like Field Medals, there’s many professional mathematicians who never even bother because that type of competition isn’t interesting to them. It’s not unreasonable to expect that professional mathematicians are able to solve these problems as well if they wanted to spend 3 days on it.

But in terms of energy per solve, humans are definitely cheaper. As you note the harder part is scaling it out but so far the AI isn’t solving problems that are impossible for humans, just that given enough time it managed to perform the same task. That’s a very promising result but supremacy is slightly a ways off for now (this AI can’t win the competition for now)

[rowanG077]

The person said typical not always the case. Just because there are obviously cases where it didn't happen does mean it it's still not typically the case.